Learning Regularization for Graph Inverse Problems
This work addresses GRIPs for applications like drug discovery and social networks, but it appears incremental as it combines existing methods rather than introducing a new paradigm.
The paper tackles Graph Inverse Problems (GRIPs) by introducing a framework that combines Graph Neural Networks (GNNs) with deep learning techniques for inverse problems, using likelihood and prior terms to fit data and adhere to learned priors, and demonstrates its effectiveness on representative problems.
In recent years, Graph Neural Networks (GNNs) have been utilized for various applications ranging from drug discovery to network design and social networks. In many applications, it is impossible to observe some properties of the graph directly; instead, noisy and indirect measurements of these properties are available. These scenarios are coined as Graph Inverse Problems (GRIP). In this work, we introduce a framework leveraging GNNs to solve GRIPs. The framework is based on a combination of likelihood and prior terms, which are used to find a solution that fits the data while adhering to learned prior information. Specifically, we propose to combine recent deep learning techniques that were developed for inverse problems, together with GNN architectures, to formulate and solve GRIP. We study our approach on a number of representative problems that demonstrate the effectiveness of the framework.